Structural color palette of disordered colloids in the Rayleigh scattering regime

Structural coloration by Rayleigh scattering is widespread in nature and holds a prominent place in various art objects over a broad period of time. Beyond the common statement that Rayleigh scattering is the primary mechanism behind the multiple colored appearances of the sky, it appears that the relationship between material parameters and the colors appearing in different observation conditions has not been thoroughly explored so far. This study provides a comprehensive overview of Rayleigh scattering-based structural colors as functions of key material properties, and introduces a scalable, environmentally friendly method to fabricate solid composites with targeted colors in both reflection and transmission. Monte Carlo light transport simulations are performed to compute the structural color palette of disordered colloids -- dielectric particles in a nonscattering matrix -- in different observation modes. We provide a range of physical parameters in which the materials exhibit the same blue color in diffuse reflection and transmission. We also show that, counterintuitively, the addition of black absorbents to the matrix of a white (opaque) material can lead to the emergence of a blue coloration in diffuse reflection, thanks to the interplay between multiple scattering and absorption. Our predictions are validated by optical experiments on colloidal suspensions of Yttria-stabilized Zirconia (ZrO$_2$:Y$_2$O$_3$) nanoparticles in aqueous solutions. The potential of Rayleigh-scattering materials for visual arts and design is further supported by realizing solid-state composites based on abundant materials, namely borosilicate clays and hybrid silica-based glasses, using soft chemistry at room temperature.